Dynamic proportional hazard rate and reversed hazard rate models

Nanda, Asok K.; Das, Suchismita

doi:10.1016/j.jspi.2010.12.025

Cited by 17 publications

(17 citation statements)

References 19 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Recalling the alternative expression of the residual entropy (19) given in (2.2) of [24], and the alternative expression of the past entropy (20) shown in (2.1) of [28], we have…”

Section: Results On Dynamic Differential Entropiesmentioning

confidence: 99%

“…The relative ratio of improvement of this system is then evaluated by means of (14). In the remaining part of this section, we restrict our attention to the special case in which X and Y satisfy the proportional hazard rates model (see Cox [19] or, for instance, the more recent contributions by Nanda and Das [20], and Ng et al [21]). Hence, assuming that G(t) = [F(t)] θ , ∀t ≥ 0, for θ > 0, θ = 1, the relative ratio defined in (14) becomes…”

Section: Examplementioning

confidence: 99%

See 1 more Smart Citation

Stochastic Comparisons and Dynamic Information of Random Lifetimes in a Replacement Model

Crescenzo

Gironimo

2018

Mathematics

View full text Add to dashboard Cite

We consider a suitable replacement model for random lifetimes, in which at a fixed time an item is replaced by another one having the same age but different lifetime distribution. We focus first on stochastic comparisons between the involved random lifetimes, in order to assess conditions leading to an improvement of the system. Attention is also given to the relative ratio of improvement, which is proposed as a suitable index finalized to measure the goodness of the replacement procedure. Finally, we provide various results on the dynamic differential entropy of the lifetime of the improved system.

show abstract

“…Recalling the alternative expression of the residual entropy (19) given in (2.2) of [24], and the alternative expression of the past entropy (20) shown in (2.1) of [28], we have…”

Section: Results On Dynamic Differential Entropiesmentioning

confidence: 99%

Section: Examplementioning

confidence: 99%

Stochastic Comparisons and Dynamic Information of Random Lifetimes in a Replacement Model

Crescenzo

Gironimo

2018

Mathematics

View full text Add to dashboard Cite

show abstract

“…This means that X 1 and X 2 satisfy dynamic proportional hazard rate model that was recently introduced by Nanda and Das (2011) where c is an increasing proportionality function of time. From Theorems 2.1, 2.2, and 2.3 in Nanda and Das (2011), the following result can be considered as an immediate conclusion of Theorem 3.1. Suppose…”

Section: Discussionmentioning

confidence: 81%

“…In view of Theorem 3.1, the result of Theorem 3.2 of Nanda and Das (2011) can be translated into the following result.…”

Section: Discussionmentioning

confidence: 99%

Some results on the relative ordering of two frailty models

2015

View full text Add to dashboard Cite

show abstract

“…It needs to be pointed out here that the dynamic proportional hazard rate and reversed hazard rate models have been studied by Nanda and Das [13]. If the covariate vector z depends on t, then we can write z = z(t), and the model reduces to m(t; z) = m 0 (t) exp[β z(t)].…”

Section: Introductionmentioning

confidence: 99%

On Dynamic Proportional Mean Residual Life Model

Nanda¹,

Das²

2013

Prob. Eng. Inf. Sci.

Self Cite

View full text Add to dashboard Cite

Recently, proportional mean residual life model has received a lot of attention after the importance of the model was discussed by Zahedi [17]. In this paper, we define dynamic proportional mean residual life model and study its properties for different aging classes. The closure of this model under different stochastic orders is also discussed. Many examples are presented to illustrate different properties of the model.for t ∈ [0, ∞) such thatF X (t) > 0. It is to be mentioned here that if the support of X is [a, b], thenF X (t) = 0 for all t > b. In such a case, Eq. (1.1) does not define m X (t) for t > b.But it is customary, in such cases, to define m X (t) = 0 for t > b; see, for instance, Shaked and Shanthikumar [16, pp. 81-82]. Thus, m X (t) 0 for all t 0.Failure time data have been modeled by using Cox's proportional hazards (PH) model; see Cox [2]. Based on the assumption of proportional mean residual life (PMRL) functions, the concept of Proportional Mean Residual Life Model, parallel to Cox's PH model, was introduced by Zahedi [17] (see also Lam [7], Oakes [14], Oakes and Dasu [15]) as(1.2)The following interpretation for the PMRL model has been given recently by Nanda, Bhattacharjee, and Balakrishnan [12]. Let a series system be formed with k components, of which one component has lifetime distribution F and the other k − 1 components have i.i.d. life distribution, which is the equilibrium distribution corresponding to F . An equilibrium distribution is obtained as a limiting distribution of a renewal process. Then the MRL function of the system so formed and the MRL function corresponding to F are proportional with constant of proportionality c = 1/k. This paper deals with the properties of the PMRL model when the constant of proportionality depends on time. Gupta, Gupta, and Gupta [4] proposed the Proportional Reversed Hazard (PRH) Model to analyze failure time data. Gupta and Wu [6] have studied some properties of the PRH model. Mi [9] has shown that if a component has a bathtub-shaped failure rate function, then MRL is unimodal, but the converse does not hold. Later, Ghai and Mi [3] developed sufficient conditions for the unimodal MRL to imply that the failure rate function has a bathtub shape. The PMRL model and its implications have been discussed by Gupta and Kirmani [5]. Nanda, Bhattacharjee, and Alam [10] have discussed some properties of the PMRL model in the context of reliability theory. The PMRL model has been extended to a regression model with explanatory variables by Magulury and Zhang [8]. If we replace c in Eq. (1.2) by some non-negative function of t, say c(t), then the corresponding equation becomes

show abstract

Dynamic proportional hazard rate and reversed hazard rate models

Cited by 17 publications

References 19 publications

Stochastic Comparisons and Dynamic Information of Random Lifetimes in a Replacement Model

Stochastic Comparisons and Dynamic Information of Random Lifetimes in a Replacement Model

Some results on the relative ordering of two frailty models

On Dynamic Proportional Mean Residual Life Model

Contact Info

Product

Resources

About